Copper-Based Diamond-like Thermoelectric Compounds: Looking Back and Stepping Forward

The research on thermoelectric (TE) materials has a long history. Holding the advantages of high elemental abundance, lead-free and easily tunable transport properties, copper-based diamond-like (CBDL) thermoelectric compounds have attracted extensive attention from the thermoelectric community. The CBDL compounds contain a large number of representative candidates for thermoelectric applications, such as CuInGa2, Cu2GeSe3, Cu3SbSe4, Cu12SbSe13, etc. In this study, the structure characteristics and TE performances of typical CBDLs were briefly summarized. Several common synthesis technologies and effective strategies to improve the thermoelectric performances of CBDL compounds were introduced. In addition, the latest developments in thermoelectric devices based on CBDL compounds were discussed. Further developments and prospects for exploring high-performance copper-based diamond-like thermoelectric materials and devices were also presented at the end.


Introduction
The attractive capability of thermoelectric (TE) materials in actualizing the conversion between temperature gradient and electrical power makes them strong candidates for waste-heat recovery as well as solid-state refrigeration [1][2][3]. The practical and widespread application of TE technology strongly relies on the development of high-performance TE materials, where the TE performance of materials is evaluated by a dimensionless figure of merit, zT = α 2 σT/κ. The TE parameters α and σ are the Seebeck coefficient and electrical conductivity which, respectively, constitute the power factor, PF = α 2 σ, used to evaluate electrical conductivity characteristics. Parameter T is the Kelvin thermodynamic temperature, while κ refers to the total thermal conductivity, which is composed of two major contributions from the charge carriers (κ E ) and the lattice (κ L ), respectively. From a computational perspective, the most ideal high-performance TE material should have a large α, high σ as well as a low κ value. What cannot be avoided is the strong coupling between thermoelectric parameters regarding carrier concentration, such as when a high σ means low α and a high κ E , limiting the improvement of zT [4][5][6]. In order to achieve high zT in traditional or emerging TE materials, various methods and approaches have been adopted to reduce the correlation between thermal and electrical properties [7][8][9], including defect engineering, size effects, alloying effect and high-entropy engineering, etc. In addition to achieving high performance, the exploration of alternative materials consists of earth-abundant and eco-friendly components to meet the sake of clean and environmental protection is also considered as one of the most popular approaches in TE field [10][11][12][13]. In recent years, diverse bulk TE materials have been widely researched, including liquid-like Cu 2 (S, Se, Te), silver-based chalcogenides, Sn(Te, S, Se), half-heuslers, etc. [14][15][16].
Quaternary Cu 2 -II-IV-VI 4 (II = Co, Mn, Hg, Mg, Zn, Cd, Fe; IV = Sn, Ge; VI = Se, S, Te) compounds with more complex tetragonal structures have also been widely studied. The distinguishing features of quaternary CBDL compounds are they possess a wider bandgap and a relatively lower carrier mobility compared with the ternary CBDL compounds [68,70,76,[94][95][96][97][98][99]. Taking the orthorhombic enargite-type Cu 2 MnGeS 4 as an example [95], the bandgap of it is~1.0 eV in the initial phase while it only converts to 0.9 eV in the Cu 2.5 Mn 0.5 GeS 4 by adjusting the ratio of Mn and Cu atoms. The large-cell Cu 10 B 2 C 4 D 13 [100][101][102][103] (B = Ag, Cu; C = Co, Ni, Zn, Cu, Mn, Fe, Hg, Cd; Q = Sb, Bi, As; Q = Se, S) tetrahedrites have even more complex crystal structures, as shown in Figure 2b,c, respectively. The featured "PGEC" framework is also displayed in the Cu 12 Sb 4 S 13 tetrahedrite, where the electric transmission is controlled by a CuS 4 network and the thermal transmission is governed by a cavity polyhedral consisting of CuS 3 and SbS 3 groups [100]. In 2013, Lu et al. [102] achieved an enhanced zT of 0.95 at 720 K in Cu 12 Sb 4 S 13 utilizing Zn-doping. Moreover, Li et al. [103] attained a high zT of 1.15 at 723 K in a porous Cu 12 Sb 4 S 13 -based material; a segmented single-leg device based on the material was successfully fabricated which realized a high conversion efficiency of 6% when the ∆T reached up to 419 K. Cu 26 P 2 Q 6 S 32 [104][105][106][107][108] (P = V, Ta, Nb, W, Mo; Q = Ge, Sn, As, Sb) colusites are other large-cell examples, which possess 66 atoms in a crystal cell while the tetrahedrites possess 58 atoms. Therefore, the common characteristic of both is their inherent low κ derived from high structural inhomogeneity [108,109]. For instance, Guilmeau's group [105] obtained the lowest κ of 0.4 W·m −1 ·K −1 at 300 K in the Cu 26 V 2 Sn 6 S 32 colusite, which was attributed to the structural complexity of colusite and mass fluctuations among the Cu, V and Sn atoms. In 2018, they further elucidated the potential mechanism related to the fountainhead of intrinsically low κ for a colusite along with the influence of antisite defects and S-vacancies on carrier concentration [105,106].  [91], Copyright 2014 American Chemical Society); (b) Cu 12 SbS 13 (reprinted with permission from ref. [110], copyright 2015 American Chemical Society); and (c) Cu 26 P 2 Q 6 S 32 (reprinted with permission from ref. [106], copyright 2018 American Chemical Society).

Material Synthesis Recipes
The synthesis process accompanied by the research and development of the material is a crucial link in obtaining superior TE materials. Therefore, while the performance of TE materials have been improved by leaps and bounds, diverse techniques for synthesizing various TE compounds are also developing vigorously. As shown in Table 1, traditional technologies such as melting, the so-called solid-state reaction, are still widely used in the preparation of high-performance TE materials. Letting nature take its course, the successful application of non-equilibrium formulations, including high-energy ball milling (BM), melt spinning (MS), self-propagating high-temperature synthesis (SHS) and solvothermal (ST) technologies in the TE field provide more options for developing the new generation of TE materials with fine multi-scale microstructures. Simple schematic diagrams of several common synthesis and preparation technologies are shown in Figure 3. High-energy ball milling, also known as mechanical alloying, has been widely adopted to assist in, or directly, synthesize TE compounds with multi-dimensional structures [111][112][113][114][115][116][117][118]. For instance, Nautiyal et al. [117] synthesized a series of polycrystalline Cu 2 SnS 3 , Cu 2 ZnSe 4 and Cu 2 ZnSnS 4 TE compounds through MA, which proved that the introduction of nanostructures into the material stabilized the disordered phase structure at low temperatures was conducive to optimizing the TE transport performance of the material. The mechanism of high-energy reaction is achieved by using the inertia between the grinding balls to cause a high-energy impact on the material particles, resulting in cold welding, fracture and re-welding between the particles, leading to further crushing [114]. In addition, most of the BM process involves dry grinding in protective gas to ensure that the collision energy among balls can be effectively applied to the ground powders, and sometimes ethanol and other solvents are used as grinding media. After BM, the fine structure and even nano-powders existing in the material can effectively enhance the phonon scattering and significantly reduce the κ. BM has the advantages of high synthesis efficiency, easy operation, high cost-efficiency and the ability to synthesize thermoelectric materials in large quantities. It is usually used to produce multi-dimensional structure [115], synthetic compound [111,116,117] and mix composites [118] in the TE industry.
Melt-spinning technology is an effective approach to achieve rapid solidification by injecting a molten alloy flow into a rotating and internally cooled roller [119], as shown in Figure 3. When the melt contacts the roller, the melt will undergo rapid solidification or even amorphous transformation accompanying the rapid transfer of heat and will be produced in the form of thin strips or ribbons [119][120][121]. The microstructure, that depends on local temperature and cooling rate, can be easily controlled by adjusting the machining parameters in the process of MS [119,122]. Previous studies have shown that a large number of refined microstructures and nano-grains can be introduced in TE compounds by MS, such as SnTe, BiSbTe, PbTe and skutterudite, etc., [120,[123][124][125]. In 2019, Zhao's group [121] successfully prepared Cu-Te alloy ribbons with nanocrystalline structures using MS, and achieved the lowest κ of 0.22 W·m −1 ·K −1 in the Cu 2 SnSe 3 -based composite.
The self-propagating high-temperature synthesis starts with the heating of a small part of the sample at a point, and then the combustion wave spreads along the material to gradually realize the synthesis of the material in an extremely short amount of time [64,126], as shown in Figure 3. In 2014, Su et al. [126] successfully applied SHS to the preparation of various TE compounds for the first time, including Cu 2 SnSe 3 , CoSb 3 , Bi 2 (Te, Se) 3 , SnTe, Mg 2 (Sn, Si), etc. As the combustion wave spreads across the whole sample, it plays a role in purifying the material and maintaining its stoichiometry [126,127]. The most attractive aspect of SHS is its rapid one-step process, which can be expanded and completed with minimal energy. This feature makes it popular in the synthesis of a variety of CBDL compounds [63,64,127,128]. The main shortcoming of the self-propagating hightemperature synthesis process is that the reaction is so rapid that the sintering size of the sample is difficult to control, requiring secondary processing to ensure the quality of the materials [64,126]. For subsequent measurements and characterizations, dense block TE materials are generally manufactured using sintering technology, including HP and SPS (also known as plasma-activated sintering (PAS)). In most cases, the procedure of sintering is the last step of fabrication, as shown in Table 1, which can strengthen the densification of products and further purify the phases.
In addition, hydrothermal as well as solvothermal reactions are very efficient approaches to preparing refined materials with controllable dimensions and morphologies through the chemical synthesis process [42,45,48,[129][130][131][132][133]. In the process of ST, the stoichiometric precursor material required for the synthetic material is first dissolved in the aqueous solution, and then the internal reaction conditions, such as the pressure, pH value and additive concentration, are strictly controlled to make it react in a sealed autoclave [130,131,[134][135][136]. Although the operation is more complex compared to the physical methods mentioned above, controllable thermoelectric compound nanostructures can be synthesized through a wet process, which has the advantages of a low synthesis temperature and fine grain size. It is also worth noting that some the morphologies and sizes of the products can be greatly modified by external conditions, such as the ultrasonic mixture pretreatment time, and the reaction temperature and time [131]. For instance, Wang et al. [136] synthesized the monodispersed Cu 2 SnTe 3 nanocrystals (~25 nm) using hot-injection synthesis for the first time, in which the Te precursor was selected by dissolving TeO 2 in 1-dodecanethiol and the reaction solvent was a Cu-Sn complex solution. Moreover, Wei et al. [135] synthesized Cu 3 SbSe 4 hollow microspheres dispersed with TiO 2 by a procedure of microwave-assisted hydrothermal synthesis. One advantage of chemical synthesis is that it can control the doping of foreign ions and optimize the grain orientations of nanostructures, which has an important impact on adjusting the carrier concentration and improving phonon scattering [43,129,132,135,136].
In recent years, additive manufacturing [137,138] and machine learning [14,[139][140][141][142][143][144], as emerging intelligent industries, have gradually entered the thermoelectric field, which opens a novel and convenient means to exploring multi-phase space. Referring to diverse indicators closely related to material properties, a series of high-performance CBDL compounds have been discovered. For instance, Zhang's group [139] investigated and predicted the electronic structures and the TE transport behaviors of ABX 2 materials using a high-throughput (HTP) framework, as shown in Figure 4a. Taking the energy position of the band edge as an indicator, Chen's team [140] verified the HTP strategy with the bandgap as an indicator by screening out the potential high-performance n-type TE compounds from Cu-containing chalcogenides, as shown in Figure 4b. In addition, Shi et al. [145] proposed a new performance indicator, shown in Figure 4c,d, for guiding the discovery of TE compounds with low κ. The new indicator referred to the number mismatch (δ) between anions and cations. It should also be noted that since the difference of atomic mass was not considered, the indicator was applicable to compound families with the same elements but different compositions. It was well demonstrated in the Cu-Sn-S systems shown in Figure 4d. The high-performance thermoelectric material screening workflow for ternary compounds ABX 2 with diamond-like structures, reprinted with permission from ref. [139], copyright 2019 American Chemical Society; (b) workflow of the HTP screening process in Cu-containing metal chalcogenides, reprinted with permission from ref. [140], copyright 2022 American Chemical Society. Room temperature κ L varying with number mismatch in (c) ternary Cu-and Ag-based chalcogenides; and (d) Cu-Sn-S compounds, reprinted with permission from ref. [145], copyright 2020 the Springer Nature.

Strategies for Optimizing the TE Performances of CBDL Compounds
There are two main basic principles for achieving high-performance TE materials, one of which is to maximize the PF while the other is to minimize the κ L . One of the typical characteristics of CBDL compounds is that the highly degenerated valence band results in the compound possessing a high Seebeck coefficient. The common defect for most CBDL compounds is that they generally have low carrier concentrations at low temperatures and high κ L in their initial form. Therefore, trying to promote or maintain PF is the critical issue in the development of high-performance CBDL compounds while reducing the κ L .

Optimization in Carrier Concentration
As most TE materials have an optimal carrier concentration in the range of 10 19 to 10 21 cm −3 , one of the most common approaches to maximizing the PFs of TE materials is tuning the carrier concentration [4,5]. For optimizing the carrier concentration in CBDL compounds, a quantity of impurities with different functions has been introduced into pristine compounds. Successful cases among Cu(In, Ga) 1−x N x Te 2 (M = Ag, Zn, Ni, Mn, Cd, Hg, Gd) [23,34,[146][147][148][149][150][151], Cu 1−x Fe 1+x S 2 [152], Cu 3 Sb 1−x N x Se 4 (N = As, Zr, Hf, Al, In, Sn, Ge, Bi, La) [42,43,113,115,132,153,154] and Cu 2 Cd 1−x In x SnSe 4 [155] have demonstrated that doping towards a higher charge-carrier density can effectively improve the electrical performances of the compounds. In addition, introducing vacancies is also another available approach to optimizing the electrical transport properties as well as minimizing the κ L . On the one hand, as the most common form of p-type doping, Cu vacancy has been widely created in CBDL compounds owing to the small formation energy of defects, as seen in Cu 12−x N x Sb 4 S 13 (N = Cd, Mn, Ge, Fe, Co, Sn, Ni, Bi, Zn) [98,156], Cu 1−x (In, Ga)Te 2 [40,157,158] and Cu 3−x SbSe 4 [159]. On the other hand, it is feasible to use anion vacancies for donor doping, as displayed in Cu 2 ZnGeSe 4−x S x [160], CuFeS 2−x [161], Cu 12 Sb 4 S 13−x Se x [100] and Cu 2 FeSnS 4−x [162].

Modulation Doping
It should be pointed out that the effect of traditional doping by substituting host atoms by alien ones is fettered by the solubility limit, and worse still, it is easy to cause intense charge-carrier scattering at room temperature, resulting in a loss of electrical transport performance [7]. Compared with traditional doping, modulation doping can effectively avoid the above problems. It is usually designed as a composite composed of two kinds of nanoparticles, and only one of them contains a doping agent [86]. Recently, an unconventional doping (UDOP) strategy was proposed by Zhou et al. [27,28,163] supported this view, where the increase in the vacancies concentration was obtained from an Sb vacancy stabilized by Al rather than alien atoms. Combined with an optimized hole concentration (3.1 × 10 20 ·cm −3 ) and a maintained carrier mobility, a considerably high average PF of 19 µW·cm −1 ·K −2 was obtained in the temperature range of 300-723 K [27]. In contrast to the conventional doping method (Figure 5a), the carrier concentration and carrier mobility decouple by vacancies in the route of UDOP (Figure 5b). In other words, it can be considered that in the purposeful doping process, the doping additive itself does not provide carriers, but acts as a "stabilizer" of the cationic vacancy (Figure 5c-e), which actually offers additional holes for p-type conductive semiconductors. It has been proved that the modulation-doping strategy can be used to not only improve the PF of CBDL compounds, but also to maintain the carrier mobility of various compounds requiring a high carrier concentration.

Pseudocubic Structure
Apart from obtaining an optimal carrier concentration, the regulation of PF is also linked with the electronic band structure [5,7,8]. The high band convergence (N v ) originating from high symmetric crystal structures is beneficial for obtaining large α and high σ. Similarly, the CBDL compounds derived from the high-symmetry cubic phase, ensures that they possess highly degenerate valence bands [18,32,33]. In particular, Zhang et al. [31] proposed a pseudocubic strategy were the PF could be optimized to the greatest extent by pruning the band split-off, which was also considered as an efficient approach to exploring and screening high-performance non-cubic TE compounds. As shown in Figure 6a,b, when the valence band-splitting energy ∆ CF approximates to zero, this means that the distortion parameter η = c/2a approaches one; in other words, the bands are in a degenerate state at this time, which can trigger the maximum PF. The pseudocubic approach, also known as the unity-η rule (η = c/2a), has been successfully applied to screen out high-performance tetragonal CBDL compounds [23,35,76,97]. For instance, Li et al. [97] found that the ∆ CF of Cu 2 ZnSnSe 4 could be appropriately tuned by applying the proper strain, which provides an alternative way to improve the thermoelectric properties of the compound. As a systematic strategy, the unity-η rule is used to qualitatively guide the evaluation and manipulation of TE diamond-like lattices. For instance, the distortion parameter η, as a function of the cell parameter a, for tetragonal diamond-like chalcogenides [32] is shown in Figure 6c. It should be noted that the pseudocubic approach is limited to low-symmetry material with an ideal bandgap and a low κ L [7]. KGaA, Weinheim. The c and a are the lattice constants. Γ 4v is a nondegenerate band, and Γ 5v is a doubly degenerate band. ∆ CF is the crystal field-induced energy split at the top of the Γ 4v and Γ 5v bands; (c) distortion parameter η as a function of the lattice parameter a, reprinted with permission from ref. [32], copyright 2018 Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.

Softening p-d Hybridization
It is well known that the p-d hybridization in CBDL compounds is very strongly attributable to the quite small separation energy among the atomic levels of chalcogen p-orbitals and Cu-3d states [91,99,164]. For most CBDL compounds, the electric transport channel (mostly the valence band maxima, VBM) is regarded as being constructed by Cu-X bonds [18,22]. The chemical bonding and the electronic structure in TE materials are closely linked to their internal charge carriers and phonon transport behaviors. Therefore, the regulation of p-d hybrid strength potentially serves as an adjustable critical parameter in adjusting the properties of CBDL compounds. Taking Cu 2 SnSe 3 [25] as an example in Figure 7a, the VBM is mostly occupied by the p-d hybridization from Cu-Se bonds, which acts as the charge-conduction pathway as well as a structural retainer. In contrast, the p-orbitals of Sn atoms contribute little to the occupied states while the conductive band is primarily dominant. Similarly, the Cu-X conduction channel has also been demonstrated in some other CBDL compounds, such as CuGaS 2 [164], Cu 3 SbSe 4 [24], Cu 2 CdZnSe 4 [70], etc. The Cu 3 SbSe 4 diamond-like compound with a small bandgap is also an example influenced by the strong relativistic orbital-contraction effect [164,165]. Softening p-d hybridization, as an active strategy, has been adopted to synergistically improve the electronic and thermal transport performance of Cu 3 SbSe 4 via Ag-doping [49,166], as shown in Figure 7b. Zhang et al. [49] discovered that the PF of Cu 3 SbSe 4 was significantly enhanced by changes in the bandgap and the density of states caused by the softening of p-d hybridization, which, accompanied by Ag-doping, induced large strain fluctuations in some local structural distortions and resulted in greatly reduced κ L . In addition, Ge et al. [53] introduced an abnormally high concentration of indium in CuFeS 2 compound, as shown in Figure 7c-e; the indium was not fully ionized to In 3+ cation when on the Cu sublattice and existed mainly in the In + oxidation state. The latter, with 5s 2 lone-pair electrons, could cause strong local bond distortions, thereby softening the In-S and Cu-S bonds and introducing localized low-frequency vibrations [89]. Therefore, a low κ L value of 0.79 W·m −1 ·K −1 (Figure 7f) and a high zT value of 0.36 were recorded at 723 K in Cu 1−x In x FeS 2 samples.

Point-Defect Scattering
In the thermoelectric field, defect and nanostructuring engineering have been widely adopted to optimize the thermoelectric performance enhancement of TE materials, especially the dislocations and nanostructured interfaces which involve the scattering of lowand mid-frequency phonons, have received more attention [6]. In the process of improving the TE performance for CBDL compounds, the existence of point defects plays a more important and beneficial role in phonon scattering than in affecting the electrical behavior. There are two main types of influence on κ L originating from point defects in TE materials: the mass fluctuation ( Figure 8a) and strain field fluctuation (Figure 8b) among the host and guest atoms. Shen et al. [40] testified that substitutional defects of Ag Cu in CuGaTe 2 could reduce the κ L more efficiently than substitutional defects of Zn Ga or In Ga at the equivalent concentration, which was attributable to the larger mass fluctuation. When the dominant point defects are vacancies, the types of scattering inflected by the strain and mass fluctuations can be maximized [5]. Thus, the compounds with an intrinsic high concentration of cation vacancies, such as In 2 Te 3 and Ga 2 Te 3 , were introduced in CuGaTe 2 to depress the κ L of the matrix phase by constituting solid solutions [80]. Additionally, an elaborate investigation about the room temperature κ for cation-substituted Cu 2 ZnGeSe 4−x S x compounds displayed a reduction of 42% for κ L , where the reduction caused by mass contrast accounted for 34% and the remaining 8% was caused by strain fluctuations [160]. In their latest study, Xie et al. [151] observed the off-centering effect (Figure 8c) of an Ag atom by investigating the thermal transmission behaviors in Cu 1x Ag x GaTe 2 as well as in CuGa 1x In x Te 2 . It is obvious that the off-centering behavior of the Ag atom means a new phonon scattering mechanism is brought about by point defects, where the Ag-alloyed solid solutions resulted in an extremely low κ L , which was attributed to crystallographic distortion and extra-strong acoustic-optical phonon scattering, as shown in Figure 8d. Moreover, it can also be seen that a modified Klemens model was developed by integrating the off-centering effect and alloy-scattering with the crystallographic distortion parameter (η), which can be used as an indicator to predict the κ of diamondoid solid solutions.

Nanostructure Engineering
Controlling the nanostructures of TE materials is also an effective approach to enhancing phonon scattering through realizing an all-scale hierarchical architecture in TE materials. Zhang et al. [26] adopted a quinary alloy compound system with a complex nanosized strain-domain structure in CuGaTe 2 (Figure 9a), which made the room-temperature κ decline from 6.1 W·m −1 ·K −1 for the initial compound to 1.5 W·m −1 ·K −1 for the Ag and In co-doped sample. Wang et al. [167] achieved low κ values of 0.491 W·m −1 ·K −1 and 0.481 W·m −1 ·K −1 in Cu 3 Sb 0.92 Sc 0.08 Se 4 and Cu 3 Sb 0.92 Y 0.08 Se 4 at 623 K, respectively, with a constructed multiscale heterostructure. In 2021, Hu et al. [103] designed pore networks for tetrahedrite Cu 12 Sb 4 S 13 -based TE materials using a BiI 3 sublimation technique, as shown in Figure 9b, which led to a hierarchical structure which contained pores, pore interfaces, point defects, and granular precipitates. The effect of various scattering mechanisms on phonon-transport behaviors for Cu 12 Sb 4 S 13 -based samples are shown in Figure 9c,d. First, the existence of specially designed pores and pore interfaces reduced the κ L of samples with 0.7 vol% annealed pores (AP) by about 36%. Furthermore, Cu 1.8 S precipitates, point defects involved Ni-alloying and Bi-doping, dislocations, the solid solution of impurity Cu 3 SbS 4 phase as well as volume expansion also contributed to the reduction of κ L because they realized full-scale phonon scattering in the TE sample. Consequently, a~72% reduction in the κ L was obtained for samples with 0.7 vol% AP with the addition of a small amount of BiI 3 . Moreover, previous works demonstrated that high-density stacking faults (SFs) could be realized in doped Cu 2 SnSe 3 [62,66,168], as shown in Figure 9e-g, which also caused strong scattering of phonons as a phonon-scattering center. In addition, solvothermal synthesis [43,134,135,153] and ball milling [113,115] are effective and convenient approaches to constructing nanostructures for TE materials.

Nanocomposite
Compositing with uniformly dispersed nanoinclusions, secondary phases or nanoparticles has been widely considered as a predominant and effective strategy to optimize TE performance in CBDL compounds [27,47,67,118,128,[169][170][171][172]. Nanoparticles (NPs) introduced in composites can be effectively used as intermediate frequency phonons scatter centers and diminish κ L [5]. Sun et al. successfully incorporated ZnO [173] and Nb 2 O 5 [174] NPs into the grain boundaries of Cu 11.5 Ni 0.5 Sb 4 S 13 compounds via mechanical alloying and spark plasma sintering, respectively, and the both composites achieved a reduced κ and high zTs. In our previous work, we also introduced graphene nanosheets or SnTe NPs into Cu 3 SbSe 4 through ball milling and realized the optimization of thermoelectric properties. Hu et al. [175] obtained a relatively low κ of 0.9 W·m −1 ·K −1 at all temperatures in Fe 2 O 3 -dispersed Cu 12 Sb 4 S 13 tetrahedrite via the combination of nanostructuring and defect engineering (Figure 10a-e). As shown in Figure 10a-d, dislocations along with diverse nanostructures, such as NPs, nanotwins and nanoprecipitates, were introduced into Cu 11.5 Ni 0.5 Sb 4 S 13 by compositing magnetic γ-Fe 2 O 3 NPs, which realized all-scale hierarchical phonon scattering in the samples, making the zT reached up to~1.0 (Figure 10f). For reducing κ L , Li et al. [39] synthesized CuInTe 2 -based compounds with in-situ formed InTe nanostrips, which wrapped the nanodomains (Figure 10g-j) and resulted in the reduction of κ L by a factor of~2 compared to parent compound. It is notably anticipated that the content, dimensions and especially distribution of nano-additives in composites have an important impact the effective regulation of TE performances. (d) frequency-dependent accumulative reduction in the lattice thermal conductivity of the EMT-corrected sample with 0.7 vol% AP due to various scattering mechanisms. Reprinted with permission from ref. [103], copyright 2021 Wiley-VCH GmbH; (e) calculated generalized stacking fault energies as a function of normalized Burger's vector b <010> in Cu 2 SnSe 3 -based system, the insert was the high-dense stacking faults (SFs) in (Fe, Ag, In)-doped Cu 2 SnSe 3 . Reprinted with permission from ref. [66], copyright 2022 Elsevier Ltd. High-dense SFs in (f) (Ag, Ga, Na)-doped (reprinted with permission from ref. [62], copyright 2021 Wiley-VCH GmbH); and (g) Ni-doped (reprinted with permission from ref. [168], copyright 2021 American Chemical Society) Cu 2 SnSe 3 .

Lattice Softening Effects
The internal strain fluctuation induced by lattice defects, such as nanoprecipitates and dislocations, can locally shift the phonon frequencies in the TE material, which in principle can bring about lattice-softening accompanied by phonon scattering owing to changes in phonon speed, as shown in Figure 11a. In several cases, improvements in TE performance ascribed to lattice-softening through the introduction of vacancies or alloying have been presented [176][177][178], such as SnTe with AgSbTe 2 alloying, and the lattice-softening effect in Cu 2 Se, as shown in Figure 11b. In 2019, Hanus et al. [179] authenticated that the changes of thermal transport behavior in the PbTe system were attributable to the lattice-softening through alloying or lattice defects, and pointed out that the modulation of lattice stiffness had a significant impact on the phonon transport in some states. In addition, Muchtar et al. [176] introduced lattice-softening into SnTe by inserting Ti and Zr atoms, which effectively suppressed the phonon group velocities and reduced the κ. Moreover, Snyder et al. [180] found the lattice-softening effect induced by charge-carrier-mediated in several high-performing (zT > 1) TE materials (such as SnTe, PbTe, Nb0 .8+x CoSb, etc.) contributed more than 20% to zT. Simultaneously, the results shown in Figure 11c indicate that a strong dependence of sound velocities v s on Hall charge-carrier concentration n H was observed in each compound in which the measured v s significantly decreased with increasing n H . Lattice-softening effects also have been successfully used to improve the TE performances of CBDL compounds. Pöhls et al. [181] demonstrated that the Li-induced phonon-softening effect was feasible to enhance the TE performance of chalcopyrite CuGaTe 2 . Xie et al. [38] obtained an extremely low κ L of 0.47 W·m −1 ·K −1 at 850 K in Ag-doped CuInTe 2 compound that was attributed to strong interactions among low-frequency optical phonons derived from the weakened Ag-Te bonds, as shown in Figure 11d.  Reprinted with permission from ref. [180], copyright 2021 Elsevier Inc.; and (d) contribution of distinct scattering mechanism to the κ L of Cu 0.8 Ag 0.2 InTe 2 . Here the U, B, P and R represent Umklapp scattering, grain-boundaries scattering, point-defect scattering, and phonon-resonance scattering, respectively; the insert shows the calculated phonon relaxation times τ versus phonon frequency ω for Cu 0.8 Ag 0.2 InTe 2 with different scattering mechanisms. Reprinted with permission from ref. [38], copyright 2020 The Royal Society of Chemistry.

Entropy Engineering
In the process of optimizing the electrical and thermal transport properties of TE materials, it is never just to adjust one of them individually. To some extent, the above optimiza-tion process can realize the decoupling of electron and phonon transmission. Entropy engineering provides a new pathway to synergistically optimize the electrical, thermal, and mechanical properties for promoting the development of CBDL compounds [15,41,90,182,183]. Through synergistic regulation, Xie et al. [41] achieved a maximum zT of 1.5 at 850 K in the quinary (Cu 0.8 Ag 0.2 )(In 0.2 Ga 0.8 )Te 2 compound, in which Ga-substituted In and Agsubstituted Cu effectively optimized the electrical and thermal transport properties, respectively. In addition, Cai et al. [183] obtained a high zT of 1.02 in CuInTe 2 compound, which was attributed to the reduction of κ by devising a high-entropy structure as well as by improving the carrier mobility by one order of magnitude. In many cases long before that, Liu et al. [15] utilized the entropy attribute as the comprehensive gene-like performance indicator to screen and devise TE materials with high zT. As can be seen in Figure 12a,b, a special example can be noted that when multi-component alloy elements are adopted in compounds, the configurational entropy can especially be changed. For a given multicomponent material, the maximum entropy lies on the solubility parameter δ of the whole material, which is linked to the mismatch of the atomic radius, shear modulus and lattice constant in the material, as shown in Figure 12c. Instructing with δ-criterion (Figure 12d), representative multi-component (Cu/Ag)(In/Ga)Te 2 -based CBDL compounds with zTs approaches to 1.6 were screened out owing to the optimization of entropy.

Progressive Regulation Strategy
The progressive regulation strategy can be realized via integrating point defects and microstructure engineering. Luo et al. [30,36] successfully acquired high-performance CuInTe 2 compounds by integrating the cation/anion substitution and in-situ oxidation, as shown in Figure 13a. Taking the in-situ substitution reaction between CuInTe 2 and ZnO additive as a case [36], the priority generation of acceptor defects Zn − In significantly optimized the PF while the In 2 O 3 nanoinclusions incurred by the in-situ reaction led to a low κ of CuInTe 2 . Through triple doping in Cu 2 SnSe 3 , Hu et al. [62] obtained an excellent zT of 1.6 at 823 K in cubic Cu 1.85 Ag 0.15 (Sn 0.88 Ga 0.1 Na 0.02 )Se 3 and a decent zT ave of 0.7 from 475 to 823 K in Cu 1.85 Ag 0.15 (Sn 0.93 Mg 0.06 Na 0.01 )Se 3 via synergistic effects. As shown in Figure 13b, during the management process from the initial phase to (Ag, Ga, Na)-doped Cu 2 SnSe 3 , the gradually improved zT originated from symmetry enhancing, alloying scattering and dislocation/nanoprecipitate construction, respectively. Similarly, synergistically optimized CuGaTe 2 [135] (Figure 13c), Cu 3 SbSe 4 nanocrystals with Cu 2−x Se in-situ inclusions [48], CuIn 1−x Ga x Te 2 :yInTe with in situ formed nanoscale phase InTe [39], Cu 2 SnSe 3 with CuInSe 2 alloying [184], etc, demonstrated that the progressive and collaborative optimization strategies have been widely applied in CBDL materials. Reprinted with permission from ref. [30,36], copyright 2015 Elsevier Ltd. All rights reserved and 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim; (b) quality factor analysis on the relationship of chemical potential η versus zT in Cu 2 SnSe 3 -based compounds. Reprinted with permission from ref. [62], copyright 2021 Wiley-VCH GmbH; and (c) schematic diagram illustrating various phonon scattering mechanisms and the electron localized region near carbon particles (CPs) within the CuGaTe 2 +x wt% CPs sample. Reprinted with permission from ref. [135], copyright 2020 The Royal Society of Chemistry.

CBDL-Based TE Devices
For practical TE applications, moving from high-performance materials to highefficiency devices is of great significance. CBDL compounds conform to the concept of green environmental protection and have great practical application value while the absence of n-type conductive compounds greatly hinders the manufacture and application of CBDL-based TE devices. During the journey of device development, researchers have made a lot of efforts. In 2017, Qiu et al. [185] manufactured a CBDL-based TE module via integrating high-performance n-type Ag 0.9 Cd 0.1 InSe 2 and p-type Cu 0.99 In 0.6 Ga 0.4 Te 2 leg, respectively, as shown in Figure 14a. The output power of module reached 0.06 W under a temperature difference of 520 K (Figure 14b), demonstrating that diamond-like compounds are also potential candidates for TE applications. On the foundation of obtaining high-performance in (Sn, Bi)-codoped nanocrystalline Cu 3 SbSe 4 materials, Liu et al. [153] fabricated a hot pipe integrated by a series of ring-shaped Cu 3 Sb 0.88 Sn 0.10 Bi 0.02 Se 4 -based TE modules (Figure 14c), which can be used for the purpose of retrieving the waste heat from exhaust gas pipes in vehicles. Moreover, Li et al. [103] synthetized a segmented Cu 12 Sb 4 S 13 -based single-leg module, which had a superior conversion efficiency η of 6% at ∆T = 419 K, as shown in Figure 14d,e. Recently, the Cu 3 SbS 4 -based single-leg module synthetized by Zhang et al. [28] approached a conversion efficiency η of 2% with ∆T = 375 K, which reached to 5.5% predicted by the COMSOL simulation analysis (Figure 14f,g). Apart from realizing excellent TE efficiency, good thermal stability is also crucial for the manufacturing of TE devices. In practice, the volatilization induced softening and decomposition is the core issue for thermoelectric selenides and sulfides working at elevated temperatures. In the latest research from Zhou's group [163] demonstrated that the compositing of CuAlS 2 significantly optimized the thermal stability of Cu 3 SbSe 4 -based compounds by pushing the decomposition temperature to a higher value, while also greatly improving the mechanical properties of the material. Eventually, a maximum η over 3% was achieved at a ∆T = of 367 K and an I = 0.8 A. Based on the above research, it seems that CBDL has considerable TE performance and has gradually attracted researchers' attention in the field of practical TE applications.

Conclusions and Perspectives
By reviewing the research on copper-based diamond-like thermoelectric materials, it has been found that diverse compounds appear to have excellent TE performances as well as possessing zT higher than unity and an even approach to two. Advanced approaches to guide the development of new high-performance CBDL materials have been found, such as machine learning, high-throughput and union-η rules. There are also various approaches to improving the TE properties of CBDL compounds. It is worth considering that, during the process of optimizing electrical and thermal transport behaviors of TE materials, the regulation is never carried out separately, but that coordination and unification of the two are sought. Based on the efforts of researchers, the CBDL compounds have been greatly developed. There is no escaping the fact that the softening and decomposition of Cu-based compounds occurs when the compounds are exposed to high temperatures. Therefore, compared with practical materials, the CBDL compounds still have great room for improvement.
Considering practical applications, it is of great significance to shift our focus from high-performance TE materials to highly efficient devices. The integration for TE equipment requires both high-performance n-type and p-type legs. Currently, CBDL compounds are mostly p-type materials, while the further development of n-type CBDL compounds is beneficial for its TE application. In addition, in the research and development process of TE devices, it is also necessary to consider the comprehensive properties such as thermal stability, processability and self-compatibility. Therefore, the feasibility of manufacturing efficient TE devices based on CBDL materials remains a highly challenging issue.
The exploration of material properties is still ongoing, and the practical application of devices also needs to be developed. There has been a deep understanding of the transport mechanism of TE materials with the iteration and update of characterization methods, accompanied by the assistance of more advanced manufacturing technologies, and that the development of high-performance TE materials and devices based on CBDL compounds has a bright future.

Conflicts of Interest:
The authors declare no conflict of interest.